Valeurs propres immergées dans le spectre continu d'une surface de Riemann
A manifold is said to be Hessian if it admits a flat affine connection and a Riemannian metric such that where is a local function. We study cohomology for Hessian manifolds, and prove a duality theorem and vanishing theorems.
In this paper, for complete Riemannian manifolds with radial Ricci or sectional curvature bounded from below or above, respectively, with respect to some point, we prove several volume comparison theorems, which can be seen as extensions of already existing results. In fact, under this radial curvature assumption, the model space is the spherically symmetric manifold, which is also called the generalized space form, determined by the bound of the radial curvature, and moreover, volume comparisons...